Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.
Computational complexityIn computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.
Particle filterParticle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system.
XilinxXilinx, Inc. (ˈzaɪlɪŋks ) was an American technology and semiconductor company that primarily supplied programmable logic devices. The company is known for inventing the first commercially viable field-programmable gate array (FPGA) and creating the first fabless manufacturing model. Xilinx was co-founded by Ross Freeman, Bernard Vonderschmitt, and James V Barnett II in the year 1984 and the company went public on the NASDAQ in the year 1990.
Minimum mean square errorIn statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated.
Circuit underutilizationCircuit underutilization also chip underutilization, programmable circuit underutilization, gate underutilization, logic block underutilization refers to a physical incomplete utility of semiconductor grade silicon on a standardized mass-produced circuit programmable chip, such as a gate array type ASIC, an FPGA, or a CPLD. In the example of a gate array, which may come in sizes of 5,000 or 10,000 gates, a design which utilizes even 5,001 gates would be required to use a 10,000 gate chip.
Analysis of algorithmsIn computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input.
Complex programmable logic deviceA complex programmable logic device (CPLD) is a programmable logic device with complexity between that of PALs and FPGAs, and architectural features of both. The main building block of the CPLD is a macrocell, which contains logic implementing disjunctive normal form expressions and more specialized logic operations. Some of the CPLD features are in common with PALs: Non-volatile configuration memory. Unlike many FPGAs, an external configuration ROM isn't required, and the CPLD can function immediately on system start-up.
Time seriesIn mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart).
Simultaneous localization and mappingSimultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. While this initially appears to be a chicken or the egg problem, there are several algorithms known to solve it in, at least approximately, tractable time for certain environments. Popular approximate solution methods include the particle filter, extended Kalman filter, covariance intersection, and GraphSLAM.
